Question

Find y as a function of x if x² y² +13 x y3+36 y=x^{7} y(1)=-9,

Answer 1

To find y as a function of x, we need to solve the given equation x^2 y^2 + 13xy^3 + 36y = x^7 for y. Here is the step-by-step process: 1) Rewrite the equation as a quadratic equation in y. 2) Use the quadratic formula to solve for y. 3) Substitute the values to find the specific solution for y.

Step-by-step explanation:

To find y as a function of x, we need to solve the given equation x^2 y^2 + 13xy^3 + 36y = x^7 for y. Here is the step-by-step process:

1. Rewrite the equation as a quadratic equation in y: (x^2)y^2 + (13x)y^3 + (36)y - (x^7) = 0.
2. Use the quadratic formula to solve for y: y = (-b ± sqrt(b^2 - 4ac))/(2a). In this case, we have a = x^2, b = 13x, and c = 36-x^7.
3. Substitute these values into the quadratic formula and simplify to obtain the two possible solutions for y.

By substituting the value x = 1 and setting y = -9, we can find the specific solution for y.